On the role of supercompact and extendible cardinals in logic

It is proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Löwenheim Theorem for second order logic, whereas the existence of extendible cardinal is equivalent to a certain compactness theorem for that logic. It is also proved that a certain axiom schema related to model theory implies the existence of many extendible cardinals.     

Bounds for certain integrals

A certain class of definite integrals is considered in which the integrand consists of a one-signed function together with another function which has a one-signed derivative in a certain interval. By examining the Cauchy form of the remainder, sets of bounds are developed which have a certain optimum property. The integrals may be multi-dimensional. The case in which the derivative component is not one-signed is briefly considered.     

基于功能不完全可加系统的系统优化

为了揭示系统的某一功能达到最优与其所有子系统为实现系统这一功能而提供的功能之间的联系,探讨了功能不完全可加系统的系统优化过程,认为可通过对系统施加调节控制作用,使系统状态成功转移到期望状态的总成本最小来实现对系统的优化.最后辅以实例.     

An instability theorem for a certain sixth order nonlinear delay differential equation

The aim of this paper is to establish an instability theorem for a certain sixth order nonlinear delay differential equation. The proof of the theorem is based on the use of Lyapunov–Krasovskii functional approach. By this work, we improve an instability result obtained in the literature for a certain sixth order nonlinear differential equation without delay to the instability of the zero solution of a certain sixth order nonlinear delay differential equation.     

Quast m-rings and their radicals

The concept, of quasi M-rings is introduced if N is a class of rings satisfying certain conditions. This concept enables us to characterize certain radical classes and also to construct new N-radicals.     

On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries

Properties of the Dirichlet problem for the Laplace equation in a bounded plane domain of a special type are studied in a certain class of solutions with power-law singularities. We prove that if a harmonic function is allowed to have a finite number of poles, then it can satisfy the trivial Dirichlet condition on certain curves of the studied family. The specified curves are selected, and it is shown that the set of those curves is dense (in a certain sense) in the studied family.     

Cohomology structure for a Poisson algebra:Ⅱ

For a Poisson algebra, we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived functor. We show that the(generalized) deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild conditions. Finally we construct a long exact sequence, and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups.     

Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials

A certain standard form is found for a complex matrix with respect to equivalent transformations by quasi-diagonal matrices. The solvability of certain matrix equations in the rings of quasi-diagonal matrices is examined using this standard form.     

某些级数的无理性

本文证明了某些与二阶线性递推数列有关的无穷级数的和的无理性．特别，推广了某些与Ｆｉｂｏｎａｃｃｉ和Ｌｕｃａｓ数列有关的无理性结果     

Arithmetical properties of finite graphs and polynomials

A study is made of asymptotic arithmetical properties of the isomorphism classes of certain types of finite graphs, and of certain polynomials over Galois fields.